**Multiplying Fractions:**
To find the product of two fractions, we multiply their numerators together and their denominators together. So, for the expression -2/3 × 3/5, we have:

(-2/3) × (3/5) = (-2 × 3) / (3 × 5) = -6/15

**Simplifying the Product:**
To simplify the product, we can cancel out any common factors between the numerator and the denominator. In this case, both -6 and 15 can be divided by 3:

-6/15 = (-6 ÷ 3) / (15 ÷ 3) = -2/5

So, the simplified value of -2/3 × 3/5 is -2/5.

**Multiplying Fractions with Whole Numbers:**
To multiply a fraction with a whole number, we can convert the whole number into a fraction by placing it over 1. So, for the expression 5/2 - 3/5 × 1/6, we can rewrite it as:

5/2 - (3/5) × (1/6) = 5/2 - (3/5) × (1/6) × (2/2) = 5/2 - (3/5) × (2/12)

**Multiplying the Fractions:**
Now, we can multiply the fractions (3/5) and (2/12) using the method described earlier:

(3/5) × (2/12) = (3 × 2) / (5 × 12) = 6/60

**Simplifying the Product:**
We can simplify the product 6/60 by dividing both the numerator and the denominator by their greatest common divisor, which is 6:

6/60 = (6 ÷ 6) / (60 ÷ 6) = 1/10

**Subtracting the Fractions:**
Now, we can substitute the simplified product (1/10) back into the expression:

5/2 - 1/10

**Finding a Common Denominator:**
To subtract fractions, we need to have a common denominator. In this case, we can find the least common multiple (LCM) of 2 and 10, which is 10. So, we need to rewrite the fractions with a denominator of 10:

5/2 = (5 × 5) / (2 × 5) = 25/10

1/10 (already in the desired form)

**Subtracting the Fractions:**
Now, we can subtract the fractions:

25/10 - 1/10 = (25 - 1) / 10 = 24/10

**Simplifying the Result:**
To simplify the fraction 24/10, we can divide both the numerator and the denominator by their greatest common divisor, which is 2:

24/10 = (24 ÷ 2) / (10 ÷ 2) = 12/5

Therefore, the final answer to the expression 5/2 - 3/5 × 1/6 is 12/5, which can also be written as 2.

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